Semi‐Analytical Solution of Energy and Momentum Equations With Robin′s Boundary Conditions in a Microchannel Flow.
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| Title: | Semi‐Analytical Solution of Energy and Momentum Equations With Robin′s Boundary Conditions in a Microchannel Flow. |
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| Authors: | Fooladvand, Ali1 (AUTHOR), Nourazar, S. S.1 (AUTHOR) salman.nourazar@yahoo.com, Nazari-Golshan, A.2 (AUTHOR), Rabeti, Masoud3 (AUTHOR) masoud.rabeti@iau.ac.ir, Tiryakio?lu, Burhan (AUTHOR) burhan.tiryakioglu@marmara.edu.tr |
| Source: | Journal of Applied Mathematics. 7/13/2026, Vol. 2026, p1-14. 14p. |
| Subjects: | Microchannel flow, Fourier transforms, Heat transfer, Scientific method, Navier-Stokes equations, Analytical solutions, Neumann boundary conditions, Heat transfer coefficient |
| Abstract: | In this study, the nonlinear momentum and energy equations governing magnetohydrodynamic microchannel flow are solved under a Robin‐type slip boundary condition. To impose the mixed boundary conditions directly in the semi‐analytical construction, the Adomian decomposition method (ADM) is combined with the Fourier transform. The integration‐by‐parts operations in the Fourier domain make the boundary terms explicit and enable the Dirichlet, Neumann, and Robin‐type slip conditions to be incorporated into the recursive FTADM solution. The velocity and temperature solutions are validated against fourth‐order Runge–Kutta computations for the nonlinear magnetohydrodynamic Jeffery–Hamel microchannel formulation. The comparisons show excellent agreement, with maximum discrepancies of the order of 10−5 for the tested cases. The results further demonstrate the influence of the channel angle and Hartmann number on the velocity and heat‐transfer behavior while retaining a compact semi‐analytical representation of the solution. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this study, the nonlinear momentum and energy equations governing magnetohydrodynamic microchannel flow are solved under a Robin‐type slip boundary condition. To impose the mixed boundary conditions directly in the semi‐analytical construction, the Adomian decomposition method (ADM) is combined with the Fourier transform. The integration‐by‐parts operations in the Fourier domain make the boundary terms explicit and enable the Dirichlet, Neumann, and Robin‐type slip conditions to be incorporated into the recursive FTADM solution. The velocity and temperature solutions are validated against fourth‐order Runge–Kutta computations for the nonlinear magnetohydrodynamic Jeffery–Hamel microchannel formulation. The comparisons show excellent agreement, with maximum discrepancies of the order of 10−5 for the tested cases. The results further demonstrate the influence of the channel angle and Hartmann number on the velocity and heat‐transfer behavior while retaining a compact semi‐analytical representation of the solution. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 1110757X |
| DOI: | 10.1155/jama/1677092 |
